Scoring functions in the setting of ordered qualitative scales

Many decision making problems involve the use of linguistic information collected by questionnaires based on ordered qualitative scales. In such cases it is relevant how agents perceive the scales. Some of them can be considered as non-uniform, in the sense that agents may perceive different proximities between consecutive terms of the scale. For instance, in the framework of health-care and medicine, the ordered qualitative scale {poor, fair, good, very good, excellent}, used by patients to evaluate self-rated health, it could be considered as non-uniform if ‘fair’ is perceived closer to ‘good’ than to ‘poor’, or if ‘good’ is perceived closer to ‘very good’ than to ‘fair’, or if ‘very good’ is perceived closer to ‘good’ than to ‘excellent’. In order to facilitate the decision-makers to manage this ordinal information, we propose to assign numerical scores to the linguistic terms of ordered qualitative scales by means of several scoring functions. In this contribution we have introduced and analyzed several scoring functions. They are based on the concept of ordinal proximity measure that properly represents the ordinal proximities between the linguistic terms of the ordered qualitative scales.